Răspuns:
a) x = 2 ; y = -3
b) x = 3 ; y = -2
c) x = -1 ; y = 2
d) x = -1 ; y = 2
Explicație pas cu pas:
a)
{2x-3(y-2) = 19
{3(x-y)+2(x+2y) = 7 <=>
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{2x-3y+6 = 19
{3x-3y+2x+4y = 7 <=>
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{2x-3y = 13
{5x+y = 7 => y = 7-5x =>
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2x-3(7-5x) = 13 =>
2x-21+15x = 13 =>
17x = 34 => x = 2
y = 7-10 => y = -3
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b)
{-4x+3(x+2y) = -15
{3(x+y) -2(2x-y) = -13 <=>
--------
{-4x+3x+6y = -15
{3x+3y-4x+2y = -13 <=>
--------
{-x+6y = -15
{-x+5y = -13 => x = 5y+13 =>
-5y-13+6y = -15 => y = -2 =>
x = -10+13 => x = 3
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c)
{2(2x+3)-3(y-1) = -1
{3(2x+y)-2(x+y-3) = 4 <=>
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{4x+6-3y+3 = -1
{6x+3y-2x-2y+6 = 4 <=>
-------
{4x-3y = -10
{4x+y = -2 => y = -2-4x
4x-3(-2-4x) = -10 =>
4x+6+12x = -10 =>
16x = -16 => x = -1
y = -2+4 => y = 2
=======================
d)
{3(x+y-2) = 4(2x-y+3)+1
{2(2x-3y+1) = 3(3x-4y+5)+4 <=>
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{3x+3y-6 = 8x-4y+12+1
{4x-6y+2 = 9x-12y+15+4 <=>
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{5x-7y = -19
{5x-6y = -17 => x = (6y-17)/5 =>
------
5(6y-17)/5-7y = -19 =>
6y-17-7y = -19 => y = 2
x = (12-17)/5 => x = -1
